Over the last thirty years, computer tomography (CT) has gone from image reconstruction based on scanning in a slice-by-slice process to spiral scanning. From the 1970s to 1980s the slice-by-slice scanning was used. In this mode the incremental motions of the patient on the table through the gantry and the gantry rotations were performed one after another. Since the patient was stationary during the gantry rotations, the trajectory of the x-ray source around the patient was circular. Pre-selected slices through the patient have been reconstructed using the data obtained by such circular scans. From the mid 1980s to present day, spiral type scanning has become the preferred process for data collection in CT. Under spiral scanning a table with the patient continuously moves through the gantry that is continuously rotating about the table. At first, spiral scanning has used one-dimensional detectors, which receive data in one dimension (a single row of detectors). Later, two-dimensional detectors, where multiple rows (two or more rows) of detectors sit next to one another, have been introduced. In CT there have been significant problems for image reconstruction especially for two-dimensional detectors. In what follows the data provided by the two-dimensional detectors will be referred to as cone-beam (CB) data or CB projections.
In addition to spiral scans there are non-spiral scans, in which the trajectory of the x-ray source is different from spiral. In medical imaging, non-spiral scans are performed using a C-arm device.
For three-dimensional (also known as volumetric) image reconstruction from the data provided by a spiral and non-spiral scans with two-dimensional detectors, there are two known groups of algorithms: Exact algorithms and Approximate algorithms, that each have known problems. Under ideal circumstances, exact algorithms can provide a replication of an exact image. Thus, one should expect that exact algorithms would produce images of good quality even under non-ideal (that is, realistic) circumstances. However, exact algorithms can be known to take many hours to provide an image reconstruction, and can take up great amounts of computer power when being used. These algorithms can require keeping considerable amounts of cone beam projections in memory. Additionally, some exact algorithms can require large detector arrays to be operable and can have limits on the size of the patient being scanned.
Approximate algorithms possess a filtered back projection (FBP) structure, so they can produce an image very efficiently and using less computing power than Exact algorithms. However, even under the ideal circumstances they produce an approximate image that may be similar to but still different from the exact image In particular, Approximate algorithms can create artifacts, which are false features in an image. Under certain circumstances these artifacts could be quite severe.
To date, there are no known algorithms that can combine the beneficial attributes of Exact and Approximate algorithms into a single algorithm that is capable of replicating an exact image under the ideal circumstances, uses small amounts of computer power, and reconstructs the exact images in an efficient manner (i.e., using the FBP structure). Here and everywhere below by the phrase that the algorithm of the invention reconstructs an exact image we will mean that in theory the algorithm is capable of reconstructing an exact image. Since in real life any data contains noise and other imperfections, no algorithm is capable of reconstructing an exact image.
Image reconstruction has been proposed in many U.S. Patents. See for example, U.S. Pat. Nos.: 5,663,995 and 5,706,325 and 5,784,481 and 6,014,419 to Hu; U.S. Pat. Nos. 5,881,123 and 5,926,521 and 6,130,930 and 6,233,303 to Tam; U.S. Pat. No. 5,960,055 to Samaresekera et al.; U.S. Pat. No. 5,995,580 to Schaller; U.S. Pat. No. 6,009,142 to Sauer; U.S. Pat. No. 6,072,851 to Sivers; U.S. Pat. Nos. 6,173,032 and 6,459,754 to Besson; U.S. Pat. No. 6,198,789 to Dafni; U.S. Pat. Nos. 6,215,841 and 6,266,388 to Hsieh. However, none of the patents overcome all of the deficiencies to image reconstruction referenced above.